Anticipating Linear Stochastic Differential Equations Driven by a Lévy Process

2012/07/06 by Jorge A. León, León, Jorge A., David Márquez-Carreras +3
Mathematics · #60G51 (Secondary) #60H07 #60H10 (Primary) 60H05 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60G51 #msc:60H05 #msc:60H07 #msc:60H10

paper · pdf · doi:10.48550/arxiv.1207.1692

arxiv created 2012/07/06 · arxiv updated 2012/07/09

Abstract

In this paper we study the existence of a unique solution for linear stochastic differential equations driven by a Lévy process, where the initial condition and the coefficients are random and not necessarily adapted to the underlying filtration. Towards this end, we extend the method based on Girsanov transformation on Wiener space and developped by Buckdahn to the canonical Lévy space.

Related

• Nonlinear SDEs driven by Lévy processes and related PDEs
• Unique strong solutions of Levy processes driven stochastic differential equations with discontinuous coefficients
• Stochastic PDEs in S^′ for SDEs driven by Lévy noise
• Lévy Flows and associated Stochastic PDEs
• Limit theorems of SDEs driven by Lévy processes and application to nonlinear filtering problems